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Q: Compute ∮_C(1/z)dz where C is |z| = 1 (counterclockwise). Parametrize: z = e^(it), dz = ie^(it)dt, t: 0→2π. ∮1/z dz = ∫₀^(2π)(1/e^(it))ie^(it)dt = ∫₀^(2π)i dt = 2πi! (Nonzero! 1/z has no antiderivative on punctured plane!) ∮_C z dz = 0 (antiderivative z²/2!).